let the larger number be x
then the smaller is x-7
"the larger number is decreased by five, then doubled" ---> 2(x-5)
2(x-5) = x-7 +5
2x - 10 = x - 2
x = 8
Finish it up, and check
The difference of two number is seven. when the larger number is decreased by five, then doubled, it is five more than the small number. Find the numbers.
2 answers
a = larger number
b = smaller number
The difference of two number is seven mean:
a - b = 7
a - b = 7 Add b to both sides
a - b + b = 7 + b
a = 7 + b
a = b + 7
When the larger number is decreased by five, then doubled, it is five more than the small number mean:
( a - 5 ) * 2 = b + 5
Replace a = b + 7 in this equation
( b + 7 - 5 ) * 2 = b + 5
( b + 2 ) * 2 = b + 5
2 * b + 2 * 2 = b + 5
2 b + 4 = b + 5 Subtract b to both sides
2 b + 4 - b = b + 5 - b
b + 4 = 5 Subtract 4 to both sides
b + 4 - 4 = 5 - 4
b = 1
a = b + 7 = 1 + 7 = 8
a = 8
Proof:
a - b = 7
8 - 1 = 7
( a - 5 ) * 2 = b + 5
( 8 - 5 ) * 2 = 1 + 5
3 * 2 = 6
6 = 6
b = smaller number
The difference of two number is seven mean:
a - b = 7
a - b = 7 Add b to both sides
a - b + b = 7 + b
a = 7 + b
a = b + 7
When the larger number is decreased by five, then doubled, it is five more than the small number mean:
( a - 5 ) * 2 = b + 5
Replace a = b + 7 in this equation
( b + 7 - 5 ) * 2 = b + 5
( b + 2 ) * 2 = b + 5
2 * b + 2 * 2 = b + 5
2 b + 4 = b + 5 Subtract b to both sides
2 b + 4 - b = b + 5 - b
b + 4 = 5 Subtract 4 to both sides
b + 4 - 4 = 5 - 4
b = 1
a = b + 7 = 1 + 7 = 8
a = 8
Proof:
a - b = 7
8 - 1 = 7
( a - 5 ) * 2 = b + 5
( 8 - 5 ) * 2 = 1 + 5
3 * 2 = 6
6 = 6